Mathematics
For what value of k will 2k + 1, 3k + 3, and 5k − 1 be three consecutive terms of an A.P.?
1
2
4
6
Answer
We are given three consecutive terms of an A.P.:
2k + 1, 3k + 3, 5k − 1
In an arithmetic progression, the difference between consecutive terms is the same.
⇒ (3k + 3) - (2k + 1) = (5k - 1) - (3k + 3)
⇒ 3k + 3 - 2k - 1 = 5k - 1 - 3k - 3
⇒ k + 2 = 2k - 4
⇒ 2 + 4 = 2k - k
⇒ k = 6.
Hence, option 4 is the correct option.
Related Questions
For what value of p are 2p + 1, 13, 5p − 3 three consecutive terms of an A.P. ?
0
1
2
4
If the sum of first n terms of an A.P. is Sn = 5n2 + 3n, then its common difference is:
8
10
18
26
The first and the last terms of an A.P. are 1 and 11 respectively. If the sum of its terms is 36, then the number of terms is :
6
7
8
9